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from twelve? Ten and two ? Three from twelve ? Nine and three? Three and nine ? Four from twelve ? Eight and four ? Four and eight? Five from twelve ? Seven and five ? Five and seven ? Six from twelve ? Six and six ? How many sixes in twelve ? How many twos ? Seven from twelve ? Eight from twelve ? Nine ? Ten ? Eleven? Twelve ? How many ones in twelve ? Threes? Fours ? Fives ? Sevens? Eights ? Nines? Tens ? Elevens? Twelves?

15. Twelve and one, how many ? Take one from thirteen ? Take two ? Eleven and two, then? Two and eleven ? Take three from thirteen? Ten and three, then? Four from thirteen? Nine and four, then? Four and nine? Five from thirteen ? Eight and five ? Five and eight, then? Nine from thirteen? Nine and four, then? Four and nine ? Ten from thirteen? Three and ten, then? Ten and three ? Eleven from thirteen ? Two and eleven, then? Twelve from thirteen? Thirteen from thirteen? How many ones in thirteen? Twos? Threes? Fours ? Fives? Sixes ? Sevens, &c., to Thirteens ?

16. Thirteen and one, how many ? One from fourteen ? Two from fourteen? Twelve and two, then? Two and twelve ? Three from fourteen? Eleven and three, then? Three and eleven? Four from fourteen? Ten and four ? Four and ten? Five from fourteen? Nine and five ? Five and nine? Six from fourteen? Eight and six ? Six and eight ? Seven from fourteen? Seven and seven, then ? How many sevens in fourteen? Eight from fourteen ? Nine ? Ten ? Eleven ? Twelve ? Thirteen? Fourteen? How many ones in fourteen? Twos? Sevens, then ? Threes? Fours ? Fives? Sixes ? Eights? Nines ? Tens? Elevens? Twelves? Thirteens? Fourteens ?

17. How many are fourteen and one? Two from fifteen? Thirteen and two, then? Two and thirteen? Three from fifteen? Twelve and three, then? Three and twelve ? Four from fifteen? Eleven and four, then? Four and eleven? Five from fifteen? Ten and five then? Five and ten? Six from fifteen? Nine and six, then? Six and nine ? Seven from fifteen ? Eight and seven ? Seven and eight? Eight from fifteen? Nine from fifteen? Ten? Eleven? Twelve ? Thirteen? Fourteen ? Fifteen? How many ones in fifteen? Fifteen times one, then? How many twos in fifteen ? Threes? Five times three, then? Three times five? Is three times five the same as five times three ? Sixes in fifteen ? Sevens, &c., to fifteens in fifteen ?

18. Fifteen and one, how many ? Take one from sixteen? Two? Fourteen and two, then? Two and fourteen? Three from sixteen? Thirteen and three, then ? Three and thirteen? Four from sixteen? Twelve and four, then? Four and twelve ? Five from sixteen? Eleven and five, then? Five and eleven? Six from sixteen? Ten and six, then? Six and ten? Seven from sixteen? Nine and seven, then ? Seven and nine ? Eight from sixteen ? Eight and eight, then? How many eights in sixteen? Twos in sixteen, then ? Nine from sixteen? Ten, &c., to sixteen from sixteen? How many ones in sixteen? Twos? Threes? Fours? How many are four times four, then ? Fives, &c., to sixteens in sixteen?

19. Sixteen and one, how many? One from seventeen ? Two? How many are two and fifteen, then? Fifteen and two ? Three from seventeen? Fourteen and three, then ? Three and fourteen? Four from seventeen? Thirteen and four, then ? Four and thirteen? Five from seventeen ? Twelve and five, then ? Five and twelve ? Six from seventeen? Eleven and six, then ? Six and eleven? Seven from seventeen? Ten and seven, then ? Seven and ten? Eight from seventeen? Nine and eight, then ? Eight and nine ? Ten from seventeen ? Eleven? Twelve, &c., to seventeen from seventeen ? How many ones in seventeen? Twos? Threes? Fours, &c., to seventeens ?

20. Seventeen and one, how many ? One from eighteen ? Two? Sixteen and two, then? Two and sixteen? Three from eighteen? Fifteen and three, then ? Three and fifteen? Four from eighteen? Fourteen and four, then? Four and fourteen? Five from eighteen? Thirteen and five, then ? Five and thirteen? Six from eighteen? Twelve and six, then ? Six and twelve ? Seven from eighteen? Eleven and seven, then? Seven and eleven ? Eight from eighteen? Ten and eight, then ? Eight and ten ? Nine from eighteen? Nine and nine, then? How many nines in eighteen? How many are two times nine, then? Ten from eighteen? Eleven? Twelve, &c., to eighteen from eighteen? How many ones in eighteen? Twos, &c., to eighteens in eighteen?

[The last seventeen lessons should now be repeated, over and over, without the frame, till perfectly familiar. The instrument, however, should always be at hand for illustration. For, let it be steadily borne in mind, that all the answers are to be results of the workings of the child's own mind, though,

occasionally, the teacher may put them into a better form of words for him, some instances of which appear in this book. The frame will still be useful in many of the following lessons, especially when they are first recited. It should not, however, be used more frequently than is absolutely necessary. Perhaps it would be well that the members of the class should manage the frame by turns during the recitations.]

SECTION II. Explanatory. 1. What is the meaning of teen in the words fourteen, sixteen, &c.* What does fourteen signify, then ? Ans. Four and ten. Sixteen ? Eighteen? What is the contracted. or common name for oneteen ? For twoteen? Threeteen? Fiveteen? What is the meaning of ty, in the words sixty, seventy,* &c. ? What is the contracted name for twoty, or twainty ? For threety ? For fivety? How many tens in fifty, then? In twenty ? Forty? Ninety? Thirty ? [Repeat the above at the commencement of each lesson, till perfectly familiar.]

2. How many are twenty and ten? [Show 20 on the upper two wires, and 10 on the fourth wire of the frame.] Twenty and twenty ? [Show 20 on first and second, and 20 on ninth and tenth wires.] Twenty and thirty ? Twenty and fifty ? Thirty and ten? Thirty and fifty ? Thirty and twenty? Thirty and sixty ? Forty and twenty ? Forty and ten ? Forty and thirty? Fifty and thirty? Fifty and ten? Sixty and twenty? Ten and fifty? Thirty and fifty? Ten from twenty, how many ? Twenty from forty ? Thirty from seventy ? Fifty from sixty ? One hundred and two hundred ? Two hundred and two hundred ? Two hundred and five hundred ? Four hundred and two hundred ? Three hundred and four hundred ? One hundred and eight hundred ? Two hundred from eight hundred ? Three hundred from seven hundred ? Two hundred from one thousand ? Two hundred from seven hundred ?

3. Show ten on the frame. [Let the class show this by turns.] Twenty. Forty. Fifty. Seventy. Ninety. Sixteen. Eleven. Thirteen. Fifteen. Fourteen. Twelve. A hundred and sixteen. A hundred and twenty-three. Two hundred and

* See Introduction, page 12, near the bottom.

thirty-four. Three hundred and twenty-six. Six hundred and forty-five. [Continue and vary this exercise as far as necessary.]

SECTION III. Increase and Decrease by a Small Number,

without causing a change in the ty or tens. 1. Six and one, how many ? Sixteen and one ? Twenty-six and one? Sixty-six and one ? Thirty-six and one? A hundred and twenty-six and one ? Take one from seven; from seventeen; from thirty-seven; twenty-seven ; fifty-seven; a hundred and thirty-seven.

2. Five and three, how many ? Twenty-five and three ? Fifteen and three ? Fifty-five and three ? A hundred and twenty-five and three? Two hundred and thirty-five and three? Take three from eight. Three from eighteen. Three from thirty-eight. Three from fifty-eight. Three from a hundred and twenty-eight. Three from a hundred and eight. Three from five hundred and sixty-eight. Three from two hundred and eighteen.

3. Four and two, how many? Fourteen and two ? Fiftyfour and two ? Ninety-four and two ? A hundred and four and two ? Two hundred and fourteen and two ? A thousand and four and two ? Two from six ? Two from sixteen? From thirty-six ? From sixty-six ? From a hundred and sixteen?

4. Two and two, how many ? Twelve and two ? Seventytwo and two ? Thirty-two and two ? Fifty-two and two ? Twenty-two and two ? A hundred and forty-two and two ? Three hundred and forty-two and two ? A thousand and fortytwo and two ? Two from four ? From fourteen? From seventy-four ? From ninety-four ? From twenty-four ? From a hundred and forty-four ?

5. Two and three, how many ? Twelve and three ? Sixtytwo and three ? Forty-two and three ? Eighty-two and three? A hundred and fifty-two and three? Three hundred and twenty-two and three? Two from five ? From fifteen? From sixty-five? From forty-five? From a hundred and fifty-five? From three hundred and twenty-five ?

6. Three and three, how many ? Thirteen and three ? Fifty-three and three ? Ninety-three and three? Twenty-three

and three? Three hundred and sixty-three and three ? Take three from six ? From sixteen? From thirty-six ? From seventy-six ? From a hundred and six ? From a hundred and sixteen? From a thousand and sixteen ?

7. One and four, how many? Eleven and four ? Fortyone and four? Twenty-one and four ? Fifty-one and four ? Ninety-one and four? A hundred and one and four ? Six hundred and eleven and four ? Take four from five? From fifteen? From forty-five ? From two hundred and fifteen ? From two hundred and sixty-five?

8. Six and two, how many ? Sixteen and two ? Eightysix and two? Twenty-six and two ? Five hundred and six and two ? Take two from eight? From eighteen? From forty-eight? From three hundred and eighteen?

9. Two and seven, how many ? Twelve and seven? Thirtytwo and seven ? Seventy-two and seven? Four hundred and two and seven? Seven hundred and twelve and seven? Five hundred and thirty-two and seven ? Take seven from nine ? From nineteen? From thirty-nine ? From a hundred and nine? From five hundred and nineteen?

10. Two and five, how many ? Twelve and five? Twentytwo and five ? Eighty-two and five? Sixty-two and five ? A hundred and two and five? Two hundred and twelve and five ? Take five from seven? From seventeen? From twenty-seven? From fifty-seven? From a hundred and seventeen? From five hundred and seventeen?

11. One and seven, how many? Eleven and seven? Thirty-one and seven? Sixty-one and seven? Two hundred and twenty-one and seven ? Five hundred and eleven and seven? Take seven from eight? From eighteen? From seventyeight? From three hundred and eighteen?

12. Five and four, how many? Fifteen and four ? Fiftyfive and four? Two hundred and fifteen and four? Take four from nine ? From nineteen? From forty-nine? From two hundred and nineteen?

13. One and eight, how many ?. Eleven and eight ? Fortyone and eight ? Seventy-one and eight? Ninety-one and eight ? Three hundred and one and eight ? Four hundred and eleven and eight ? Take eight from nine? From nineteen? From ninety-nine ? From two hundred and nine ? From five hundred and nineteen?

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